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<div class="title">GPU/Complex.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2014 Benoit Steiner &lt;benoit.steiner.goog@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2021 C. Antonio Sanchez &lt;cantonios@google.com&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_COMPLEX_GPU_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_COMPLEX_GPU_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// Many std::complex methods such as operator+, operator-, operator* and</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// operator/ are not constexpr. Due to this, GCC and older versions of clang do</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// not treat them as device functions and thus Eigen functors making use of</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">// these operators fail to compile. Here, we manually specialize these</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// operators and functors for complex types when building for CUDA to enable</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">// their use on-device.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">// NOTES:</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">//  - Compound assignment operators +=,-=,*=,/=(Scalar) will not work on device,</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">//    since they are already specialized in the standard. Using them will result</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">//    in silent kernel failures.</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">//  - Compiling with MSVC and using +=,-=,*=,/=(std::complex&lt;Scalar&gt;) will lead</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">//    to duplicate definition errors, since these are already specialized in</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">//    Visual Studio&#39;s &lt;complex&gt; header (contrary to the standard).  This is</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">//    preferable to removing such definitions, which will lead to silent kernel</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment">//    failures.</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">//  - Compiling with ICC requires defining _USE_COMPLEX_SPECIALIZATION_ prior</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">//    to the first inclusion of &lt;complex&gt;.</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#if defined(EIGEN_GPUCC) &amp;&amp; defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    </div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment">// ICC already specializes std::complex&lt;float&gt; and std::complex&lt;double&gt;</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment">// operators, preventing us from making them device functions here.</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment">// This will lead to silent runtime errors if the operators are used on device.</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">// To allow std::complex operator use on device, define _OVERRIDE_COMPLEX_SPECIALIZATION_</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment">// prior to first inclusion of &lt;complex&gt;.  This prevents ICC from adding</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="comment">// its own specializations, so our custom ones below can be used instead.</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#if !(defined(EIGEN_COMP_ICC) &amp;&amp; defined(_USE_COMPLEX_SPECIALIZATION_))</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160; </div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">// Import Eigen&#39;s internal operator specializations.</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="preprocessor">#define EIGEN_USING_STD_COMPLEX_OPERATORS           \</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator+;  \</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator-;  \</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator*;  \</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator/;  \</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator+=; \</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator-=; \</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator*=; \</span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator/=; \</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator==; \</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="preprocessor">  using Eigen::complex_operator_detail::operator!=;</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="preprocessor">#include &quot;../../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="comment">// Specialized std::complex overloads.</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">namespace </span>complex_operator_detail {</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;std::complex&lt;T&gt; complex_multiply(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; a, <span class="keyword">const</span> std::complex&lt;T&gt;&amp; b) {</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">const</span> T a_real = numext::real(a);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  <span class="keyword">const</span> T a_imag = numext::imag(a);</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  <span class="keyword">const</span> T b_real = numext::real(b);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  <span class="keyword">const</span> T b_imag = numext::imag(b);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="keywordflow">return</span> std::complex&lt;T&gt;(</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;      a_real * b_real - a_imag * b_imag,</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;      a_imag * b_real + a_real * b_imag);</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;}</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160; </div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;std::complex&lt;T&gt; complex_divide_fast(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; a, <span class="keyword">const</span> std::complex&lt;T&gt;&amp; b) {</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  <span class="keyword">const</span> T a_real = numext::real(a);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="keyword">const</span> T a_imag = numext::imag(a);</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  <span class="keyword">const</span> T b_real = numext::real(b);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="keyword">const</span> T b_imag = numext::imag(b);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="keyword">const</span> T norm = (b_real * b_real + b_imag * b_imag);</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  <span class="keywordflow">return</span> std::complex&lt;T&gt;((a_real * b_real + a_imag * b_imag) / norm,</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;                          (a_imag * b_real - a_real * b_imag) / norm);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;}</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;std::complex&lt;T&gt; complex_divide_stable(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; a, <span class="keyword">const</span> std::complex&lt;T&gt;&amp; b) {</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="keyword">const</span> T a_real = numext::real(a);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="keyword">const</span> T a_imag = numext::imag(a);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  <span class="keyword">const</span> T b_real = numext::real(b);</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="keyword">const</span> T b_imag = numext::imag(b);</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <span class="comment">// Smith&#39;s complex division (https://arxiv.org/pdf/1210.4539.pdf),</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  <span class="comment">// guards against over/under-flow.</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">bool</span> scale_imag = numext::abs(b_imag) &lt;= numext::abs(b_real);</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="keyword">const</span> T rscale = scale_imag ? T(1) : b_real / b_imag;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="keyword">const</span> T iscale = scale_imag ? b_imag / b_real : T(1);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="keyword">const</span> T denominator = b_real * rscale + b_imag * iscale;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="keywordflow">return</span> std::complex&lt;T&gt;((a_real * rscale + a_imag * iscale) / denominator, </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                         (a_imag * rscale - a_real * iscale) / denominator);</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;}</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;std::complex&lt;T&gt; complex_divide(<span class="keyword">const</span> std::complex&lt;T&gt;&amp; a, <span class="keyword">const</span> std::complex&lt;T&gt;&amp; b) {</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="preprocessor">#if EIGEN_FAST_MATH</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <span class="keywordflow">return</span> complex_divide_fast(a, b);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keywordflow">return</span> complex_divide_stable(a, b);</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;}</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">// NOTE: We cannot specialize compound assignment operators with Scalar T,</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="comment">//         (i.e.  operator@=(const T&amp;), for @=+,-,*,/)</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="comment">//       since they are already specialized for float/double/long double within</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment">//       the standard &lt;complex&gt; header. We also do not specialize the stream</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">//       operators.</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="preprocessor">#define EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(T)                                    \</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator+(const std::complex&lt;T&gt;&amp; a) { return a; }                               \</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator-(const std::complex&lt;T&gt;&amp; a) {                                           \</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(-numext::real(a), -numext::imag(a));                                   \</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator+(const std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                 \</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(numext::real(a) + numext::real(b), numext::imag(a) + numext::imag(b)); \</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator+(const std::complex&lt;T&gt;&amp; a, const T&amp; b) {                               \</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(numext::real(a) + b, numext::imag(a));                                 \</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator+(const T&amp; a, const std::complex&lt;T&gt;&amp; b) {                               \</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(a + numext::real(b), numext::imag(b));                                 \</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator-(const std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                 \</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(numext::real(a) - numext::real(b), numext::imag(a) - numext::imag(b)); \</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator-(const std::complex&lt;T&gt;&amp; a, const T&amp; b) {                               \</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(numext::real(a) - b, numext::imag(a));                                 \</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator-(const T&amp; a, const std::complex&lt;T&gt;&amp; b) {                               \</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(a - numext::real(b), -numext::imag(b));                                \</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator*(const std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                 \</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="preprocessor">  return complex_multiply(a, b);                                                                \</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator*(const std::complex&lt;T&gt;&amp; a, const T&amp; b) {                               \</span></div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(numext::real(a) * b, numext::imag(a) * b);                             \</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator*(const T&amp; a, const std::complex&lt;T&gt;&amp; b) {                               \</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(a * numext::real(b), a * numext::imag(b));                             \</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator/(const std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                 \</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="preprocessor">  return complex_divide(a, b);                                                                  \</span></div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator/(const std::complex&lt;T&gt;&amp; a, const T&amp; b) {                               \</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="preprocessor">  return std::complex&lt;T&gt;(numext::real(a) / b, numext::imag(a) / b);                             \</span></div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="preprocessor">std::complex&lt;T&gt; operator/(const T&amp; a, const std::complex&lt;T&gt;&amp; b) {                               \</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="preprocessor">  return complex_divide(std::complex&lt;T&gt;(a, 0), b);                                              \</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="preprocessor">std::complex&lt;T&gt;&amp; operator+=(std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                     \</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="preprocessor">  numext::real_ref(a) += numext::real(b);                                                       \</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="preprocessor">  numext::imag_ref(a) += numext::imag(b);                                                       \</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="preprocessor">  return a;                                                                                     \</span></div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="preprocessor">std::complex&lt;T&gt;&amp; operator-=(std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                     \</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="preprocessor">  numext::real_ref(a) -= numext::real(b);                                                       \</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="preprocessor">  numext::imag_ref(a) -= numext::imag(b);                                                       \</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="preprocessor">  return a;                                                                                     \</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="preprocessor">std::complex&lt;T&gt;&amp; operator*=(std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                     \</span></div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="preprocessor">  a = complex_multiply(a, b);                                                                   \</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="preprocessor">  return a;                                                                                     \</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<span class="preprocessor">std::complex&lt;T&gt;&amp; operator/=(std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                     \</span></div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="preprocessor">  a = complex_divide(a, b);                                                                     \</span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="preprocessor">  return  a;                                                                                    \</span></div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="preprocessor">bool operator==(const std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                           \</span></div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="preprocessor">  return numext::real(a) == numext::real(b) &amp;&amp; numext::imag(a) == numext::imag(b);              \</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="preprocessor">bool operator==(const std::complex&lt;T&gt;&amp; a, const T&amp; b) {                                         \</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;<span class="preprocessor">  return numext::real(a) == b &amp;&amp; numext::imag(a) == 0;                                          \</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="preprocessor">bool operator==(const T&amp; a, const std::complex&lt;T&gt;&amp; b) {                                         \</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="preprocessor">  return a  == numext::real(b) &amp;&amp; 0 == numext::imag(b);                                         \</span></div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="preprocessor">bool operator!=(const std::complex&lt;T&gt;&amp; a, const std::complex&lt;T&gt;&amp; b) {                           \</span></div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="preprocessor">  return !(a == b);                                                                             \</span></div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="preprocessor">bool operator!=(const std::complex&lt;T&gt;&amp; a, const T&amp; b) {                                         \</span></div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;<span class="preprocessor">  return !(a == b);                                                                             \</span></div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;<span class="preprocessor">}                                                                                               \</span></div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;<span class="preprocessor">                                                                                                \</span></div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;<span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                                                           \</span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;<span class="preprocessor">bool operator!=(const T&amp; a, const std::complex&lt;T&gt;&amp; b) {                                         \</span></div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="preprocessor">  return !(a == b);                                                                             \</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;<span class="preprocessor">}</span></div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="comment">// Do not specialize for long double, since that reduces to double on device.</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(<span class="keywordtype">float</span>)</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(<span class="keywordtype">double</span>)</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160; </div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="preprocessor">#undef EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160; </div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  </div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;}  <span class="comment">// namespace complex_operator_detail</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;EIGEN_USING_STD_COMPLEX_OPERATORS</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="keyword">namespace </span>numext {</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;EIGEN_USING_STD_COMPLEX_OPERATORS</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;}  <span class="comment">// namespace numext</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;EIGEN_USING_STD_COMPLEX_OPERATORS</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160; </div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;}  <span class="comment">// namespace internal</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;}  <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160; </div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// !(EIGEN_COMP_ICC &amp;&amp; _USE_COMPLEX_SPECIALIZATION_)</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_GPUCC &amp;&amp; EIGEN_GPU_COMPILE_PHASE</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_COMPLEX_GPU_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
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